how can I saturate the outputs of ODE45 using event functions with odeset ?

Dear friends; I have the differential equations given as follows:

    x1'=x1*(1-x2^2)-x2
    x2'=x1
I have created an m-file which contains these differential equations and I have constrained the variables x1 and x2 to their upper and lower limits (-limit and +limit)
    function xdot=fun(t,x)

 xdot=zeros(2,1);
 xdot(1)=x(1)*(1-x(2)^2)-x(2);
 xdot(2)=x(1);
end

then I have simulated the differential equation defined in the function fun over the interval 0<=t<=20;

    x0=[0;0.25];
    [t,x]=ode45('fun',[0:0.01:20],x0);
    plot(t,x)
My problem consists in how to limit the state variable x because I have the condition
    -2<=x(1)<=2

So, how can I simulate the differential equation over the interval 0<=t<=20 with satisfying this condition, I will be very grateful if someone can help me to solve this problem using event function with odeset.

Thanks

Answer 1

[Torsten]

Your question has already been answered under

https://www.mathworks.com/matlabcentral/answers/196804-how-to-constraint-the-input-variables-of-ode45-with-the-odeset-function-nonnegative-option

Maybe you did not understand my answer ? Or I misunderstood your question ?

Best wishes

Torsten.

[yosra welhazi]

Dear Torsten,

You have told me that the input variables can be satureted using event functions, but I don't know how to do this ? this problem makes me desperate

[Torsten]

No, I answered that your problem cannot be solved.

The solution of your differential equation is fixed by the equation itself and the initial conditions you impose - you can not limit the solution by introducing artificial constraints.

Best wishes

Torsten.

Answer 2

[Jan]

Limiting the values means a discontinuity of the function, which cannot be handled by the ODE integrators, see http://www.mathworks.com/matlabcentral/answers/59582#answer_72047 .

So use an event function to detect the time, when x(1) exceed the limits.